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java.lang.Objectpapaya.SVD
public class SVD
Singular Value Decomposition.
For an m x n
matrix A
with m > n
,
the singular value decomposition is an m-by-n
orthogonal matrix
U
, an n-by-n
diagonal matrix S
, and
an n-by-n
orthogonal matrix V
so that A = U*S*V'
.
The singular values, sigma[k] = S[k][k]
, are ordered so that
sigma[0] > sigma[1] > ... > sigma[n-1]
.
The singular value decompostion always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition.
Shamelessly copied (and modified) from the
JAMA Java
Matrix package. To make things compatible with how most users use Processing, the
class take in float matrices. However, to preserve the acccuracy of the computations, the algorithm
first casts the input into a double array, prior to doing anything. All methods also return doubles; Use
Cast.doubleToFloat(double[][])
if you want/need to cast everything back to floats for
further (non-high-accuracy-dependant) processing (pun intended).
Constructor Summary | |
---|---|
SVD(float[][] AA)
Construct the singular value decomposition. |
Method Summary | |
---|---|
double |
cond()
Two norm condition number |
double[][] |
getS()
Return the diagonal matrix of singular values |
double[] |
getSingularValues()
Return the one-dimensional array of singular values |
double[][] |
getU()
Return the left singular vectors |
double[][] |
getV()
Return the right singular vectors |
double |
norm2()
Two norm |
int |
rank()
Effective numerical matrix rank |
Methods inherited from class java.lang.Object |
---|
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
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public SVD(float[][] AA)
AA
- Rectangular matrixMethod Detail |
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public double[][] getU()
public double[][] getV()
public double[] getSingularValues()
public double[][] getS()
public double norm2()
public double cond()
public int rank()
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